Question Number 62341 by Tawa1 last updated on 20/Jun/19 $$\mathrm{How}\:\mathrm{many}\:\mathrm{real}\:\mathrm{root}\:\mathrm{does}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\:\:\mathrm{x}^{\mathrm{8}} \:−\:\mathrm{x}^{\mathrm{7}} \:+\:\mathrm{2x}^{\mathrm{6}} \:−\:\mathrm{2x}^{\mathrm{5}} \:+\:\mathrm{3x}^{\mathrm{4}} \:−\:\mathrm{3x}^{\mathrm{3}} \:+\:\mathrm{4x}^{\mathrm{2}} \:−\:\mathrm{4x}\:+\:\frac{\mathrm{5}}{\mathrm{2}}\:\:=\:\:\mathrm{0}\:\:\:\:\:\:\:\mathrm{has} \\ $$ Commented by Kunal12588 last…
Question Number 127876 by Ar Brandon last updated on 02/Jan/21 $$\mathrm{Consider}\:\mathrm{the}\:\mathrm{sequence}\:\mathrm{defined}\:\mathrm{by}:\:\mathrm{0}<\mathrm{u}_{\mathrm{0}} <\mathrm{1}\:\mathrm{and}\:\forall\mathrm{n}\in\mathbb{N},\:\mathrm{u}_{\mathrm{n}+\mathrm{1}} =\mathrm{u}_{\mathrm{n}} −\mathrm{u}_{\mathrm{n}} ^{\mathrm{2}} . \\ $$$$\mathrm{1}.\:\mathrm{Show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{sequence}\:\left(\mathrm{u}_{\mathrm{n}} \right)\:\mathrm{converges}.\:\mathrm{What}\:\mathrm{is}\:\mathrm{its}\:\mathrm{limit}\:? \\ $$$$\mathrm{2}.\:\mathrm{Show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{series}\:\mathrm{with}\:\mathrm{general}\:\mathrm{term}\:\mathrm{u}_{\mathrm{n}} ^{\mathrm{2}} \:\mathrm{converges}. \\ $$$$\mathrm{3}.\:\mathrm{Show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{series}\:\mathrm{with}\:\mathrm{general}\:\mathrm{terms}\:\mathrm{ln}\left(\frac{\mathrm{u}_{\mathrm{n}+\mathrm{1}}…
Question Number 127859 by AgnibhoMukhopadhyay last updated on 02/Jan/21 Answered by liberty last updated on 03/Jan/21 $$\:\frac{\mathrm{3}−\mathrm{5i}}{\mathrm{8}+\mathrm{2i}}\:×\:\frac{\mathrm{8}−\mathrm{2i}}{\mathrm{8}−\mathrm{2i}}\:=\:\frac{\mathrm{24}−\mathrm{46i}−\mathrm{10}}{\mathrm{64}+\mathrm{4}}=\frac{\mathrm{14}−\mathrm{46i}}{\mathrm{68}} \\ $$$$\:=\:\frac{\mathrm{7}}{\mathrm{34}}−\frac{\mathrm{23i}}{\mathrm{34}} \\ $$ Terms of Service Privacy…
Question Number 62288 by 0987654321 last updated on 19/Jun/19 $${M}_{{TP}} ={Q}\frac{{D}}{{Z}}\:×\:{f}_{} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 127793 by Dwaipayan Shikari last updated on 02/Jan/21 $$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{n}}{{n}!}{cos}\left(\frac{\pi{n}}{\mathrm{5}}\right) \\ $$ Commented by Dwaipayan Shikari last updated on 03/Jan/21 $${I}\:{have}\:{found} \\…
Question Number 62241 by vishnurajput8081@gmail.com last updated on 18/Jun/19 $$\boldsymbol{{if}}\:\boldsymbol{{the}}\:\boldsymbol{{point}}\:{A}\:{B}\:{C}\:{with}\:{position}\:{vector}\: \\ $$$$\left(\mathrm{20}\hat {{i}}+\lambda\hat {{j}}\right)\:\left(\mathrm{5}\hat {{i}}−\hat {{j}}\right)\:{and}\left(\mathrm{10}\hat {{i}}−\mathrm{13}\hat {{j}}\right)\:{are} \\ $$$${collinear}\:{then}\:{the}\:{value}\:{of}\:\lambda\:{is}: \\ $$ Answered by tanmay…
Question Number 127771 by Dwaipayan Shikari last updated on 01/Jan/21 $$\frac{\mathrm{1}}{\mathrm{1}−\frac{\pi^{\mathrm{2}} }{\mathrm{1}+\pi^{\mathrm{2}} −\frac{\mathrm{2}\pi^{\mathrm{2}} }{\mathrm{2}+\pi^{\mathrm{2}} −\frac{\mathrm{3}\pi^{\mathrm{2}} }{\mathrm{3}+\pi^{\mathrm{2}} −\frac{\mathrm{4}\pi^{\mathrm{2}} }{\mathrm{4}+\pi^{\mathrm{2}} −\frac{\mathrm{5}\pi^{\mathrm{2}} }{\mathrm{5}+\pi^{\mathrm{2}} ….}}}}}} \\ $$ Commented by…
Question Number 127682 by Dwaipayan Shikari last updated on 31/Dec/20 $$\frac{\pi^{\mathrm{2}} }{\mathrm{1}+\frac{\pi^{\mathrm{2}} }{\mathrm{3}−\pi^{\mathrm{2}} +\frac{\mathrm{9}\pi^{\mathrm{2}} }{\mathrm{5}−\mathrm{3}\pi^{\mathrm{2}} +\frac{\mathrm{25}\pi^{\mathrm{2}} }{\mathrm{7}−\mathrm{5}\pi^{\mathrm{2}} +\frac{\mathrm{49}\pi^{\:\mathrm{2}} }{\mathrm{9}−\mathrm{7}\pi^{\mathrm{2}} +\frac{\mathrm{81}\pi^{\mathrm{2}} }{\mathrm{11}−\mathrm{9}\pi^{\mathrm{2}} +\frac{\mathrm{121}\pi^{\mathrm{2}} }{…..}}}}}}} \\ $$…
Question Number 62139 by hhghg last updated on 15/Jun/19 $$\mathrm{6}+\mathrm{5}>\mathrm{3}×\mathrm{5}\:\mathrm{true}\:\mathrm{or}\:\mathrm{false} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 127666 by Dwaipayan Shikari last updated on 31/Dec/20 $${Have}\:{a}\:{great}\:{year}\:{all}\:{of}\:{you} \\ $$$${It}\:{is}\:\mathrm{12}.\mathrm{20}\:{am}\:{in}\:{India}\:\left({GMT}+\mathrm{5}.\mathrm{30}\right) \\ $$$$\left(\mathrm{12}.\mathrm{20}\right)^{{T}} =\mathrm{20}.\mathrm{21} \\ $$$$ \\ $$💐🌅 Commented by Ar Brandon last…